Ultra wide bandwidth (UWB) systems have recently received considerable attention for wireless radio communication systems. Recently, the US Federal Communications Commission (FCC) has allowed UWB systems for limited indoor and outdoor applications.
The IEEE 802.15.3a standards group has defined performance requirements for the use of UWB in short-range indoor communication systems. Throughput of at least 110 Mbps at 10 meters are required. This means that the transmission data rate must be greater. Furthermore, a bit rate of at least 200 Mbps is required at four meters. Scalability to rates in excess of 480 Mbps is desirable, even when the rates can only be achieved at smaller ranges. These requirements provide a range of values for a pulse repetition frequency (PRF).
In February 2002, the FCC released the “First Order and Report” providing power limits for UWB signals. The average limits over all useable frequencies are different for indoor and outdoor systems. These limits are given in the form of a power spectral density (PSD) mask 200, see FIG. 2. In the frequency band from 3.1 GHz to 10.6 GHz, the PSD is limited to −41.25 dBm/MHz. The limits on the PSD must be fulfilled for each possible 1 MHz band, but not necessarily for smaller bandwidths.
For systems operating above 960 MHz, there is a limit on the peak emission level contained within a 50 MHz bandwidth centered on the frequency, fM, at which the highest radiated emission occurs. The FCC has adopted a peak limit based on a sliding scale dependent on an actual resolution bandwidth (RBW) employed in the measurement. The peak EIRP limit is 20log(RBW/50) dBm, when measured with a resolution bandwidth ranging from 1 MHz to 50 MHz. Only one peak measurement, centered on fM, is required. As a result, UWB emissions are average-limited for PRFs greater than 1 MHz and peak-limited for PRFs below 1 MHz.
These data rate requirements and emission limits result in constraints on the pulse shape, the level of the total power used, the PRF, and the positions and amplitudes of the spectral lines.
In UWB systems, trains of electromagnetic pulses are used to carry data. FIG. 1 shows an example symbol structure 100 of UWB signal with a one pulse per frame 101, i.e., the symbol length, a time hopping (TH) sequence of eight pulses 102 or subframes, and a subframe 103 including a TH margin. The signal comprises symbols 110 equal to a frame length, subframes 111, with a pulse position modulation (PPM) margin 112, and a TH margin 113. Instead of grouping N pulses to create a symbol of N frame durations, the frame duration is split into N subframes with 1 pulse per subframe, as shown in FIG. 1.
Many UWB signals use pulse position modulation (PPM) for modulation, and time hopping (TH) spreading for multiple access. This results in a dithered pulse train. The spectrum of the signal can be obtained by considering this dithered signal as a M-PPM signal.
If the modulating sequence is composed of independent and equiprobable symbols , then the PSD for non-linear memoryless modulation is given by Equation 1 as:
                                                        G              s                        ⁡                          (              f              )                                =                                                    1                                                      M                    2                                    ⁢                                      T                    s                    2                                                              ·                                                ∑                                      n                    =                                          -                      ∞                                                                            +                    ∞                                                  ⁢                                                                  ⁢                                  (                                                                                                                                                                  ∑                                                          i                              =                              0                                                                                      M                              -                              1                                                                                ⁢                                                                                    S                              i                                                        ⁡                                                          (                                                              n                                                                  T                                  s                                                                                            )                                                                                                                                                  2                                        ⁢                                          δ                      ⁡                                              (                                                  f                          -                                                      n                                                          T                              s                                                                                                      )                                                                              )                                                      +                                          1                                  T                  s                                            ⁢                              (                                                                            ∑                                              i                        =                        0                                                                    M                        -                        1                                                              ⁢                                                                  1                        M                                            ·                                                                                                                                                            S                              i                                                        ⁡                                                          (                              f                              )                                                                                                                                2                                                                              -                                                                                                                                    ∑                                                      i                            =                            0                                                                                M                            -                            1                                                                          ⁢                                                                              1                            M                                                    ·                                                                                    S                              i                                                        ⁡                                                          (                              f                              )                                                                                                                                                                  2                                                  )                                                    ,                            (        1        )            where M denotes the number of symbols, Ts is the symbol period or frame, and Si is the PSD of the ith symbol of the constellation.
Inherent in PPM, and as shown in FIG. 2, the first term of Equation (1) causes spectral lines which are outside the FCC mask 200. The spectrum of a signal with a 2-PPM usually contains spectral lines spaced by the PRF. Consequently, the amplitude of these spectral lines can be 10*log10(Ts−1) dB above the level of the continuous part of the spectrum. That corresponds to 80 dB for the 100 Mbps data rate mandated by IEEE 802.15a.
The FCC measurement procedures average the power of these spectral lines over the resolution bandwidth. Even then, the power level remains higher than the threshold and thus violates the FCC limits or requires a reduction of the total power. Time hopping is generally used to reduce the problem of spectral lines by reducing their number in a given frequency band. However TH does not necessarily attenuate the amplitude of the remaining spectral lines.
In a non-periodic time hopped pulse train, each individual pulse can be in one of M equally probable positions within its frame. This signal has the same spectrum as a M-PPM signal with the same PRF, fPR, and uncorrelated modulated data. Increasing M enlarges the constellation of the PPM, and therefore the number of pulse positions within the frame. If these positions are uniformly spaced within the frame, then all the spectral lines that are not a multiple of M·fPR disappear.
Instead of grouping N pulses to create a symbol of N frame durations, the former frame duration is split into N subframes with one pulse per subframe 111 as shown in FIG. 1. As a consequence, the PRF is N*fPR. Hence, this non-periodic TH pulse train is composed of N pulses per frame, and each pulse can take M positions within the duration of a subframe. The spectrum of this pulse train is the same as for a M-PPM signal with a PRF=N*fPR. As a result, the spectral lines are spaced by M*N*fPR when the M pulse positions are uniformly spaced. If M goes to infinity, which is equivalent to a uniform distribution of the pulse, then all spectral lines occur at infinite spacing and thus effectively vanish.
However, in order to consider realistic pulse trains that can be used in the generation of UWB signals, some modifications need to be made. If pulses are truly uniformly distributed within each frame, overlaps may happen at the junction between subframes when M increases. Margins or guard intervals eliminate these overlaps.
In order to modulate the symbols by PPM, additional margins are introduced between frames. However, by introducing margins, the uniform distribution of pulse positions within each subframe is destroyed, which has an impact on the spectral lines. Furthermore TH sequence is limited in time and contributes to the periodicity of the signal and undesirable spectral lines as shown in FIG. 2.
Therefore, there is a need to provide a system and method that can eliminate these undesirable spectral lines. Furthermore it is desired to influence the design of the power spectral density of the signal.